Finite Group Databasebeta

← #27305856

Subgroups — #27305856

Order 13568.

2118 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133175C211yesmaximal, characteristic
2C2×C4⋊C4×Dic53C211yesmaximal, characteristic, complemented
3C2×#16810474C211yesmaximal, characteristic, complemented
4C2×#16810470C212yesmaximal
5#20272968C211yesmaximal, characteristic, complemented
6#20272967C212yesmaximal, complemented
7#20272961C211yesmaximal, characteristic
8#20272959C212yesmaximal
9#20272957C211yesmaximal, characteristic
10#95×Dic53C212yesmaximal, complemented
11C53×#1441C211yesmaximal, characteristic, complemented
12C23×C4×D53C2211yescharacteristic
13C2×#13133175—24no—
14C2×#13133175—24no—
15C2×#13133175C418yescomplemented
16C22×C4⋊Dic53C2211yescharacteristic
17C22×C4⋊Dic53C2211yescharacteristic
18C22×#11719919C2212yes—
19C22×#11719921C2212yes—
20C22×#11719921C2212yes—
21C22×#11719921C2211yescharacteristic
22C22×#11719921C2211yescharacteristic
23C22×C4×Dic53C2212yes—
24C22×C4×Dic53C2212yes—
25C22×C4×Dic53C2211yescharacteristic
26C22×C4×Dic53C2211yescharacteristic
27C4⋊C4×Dic53—24no—
28#16810474—24no—
29#16810470—28no—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2211yescharacteristic
35C2×#13133124C2212yes—
36C22×C4⋊C4×C53C2211yescharacteristic
37C22×C4⋊C4×C53C2211yescharacteristic
38C2×#95×C53C2212yes—
39C2×#95×C53C2212yes—
40C2×#95×C53C2211yescharacteristic
41C24×D53C2311yescharacteristic
42C23×Dic53C2311yescharacteristic
43C23×Dic53C2312yes—
44C23×Dic53C2312yes—
45C23×Dic53C2311yescharacteristic
46C23×Dic53C2311yescharacteristic
47C22×C4×D53—22no—
48C22×C4×D53—22no—
49C22×C4×D53—22no—
50C22×C4×D53—22no—
51C22×C4×D53C2×C414yes—
52C22×C4×D53D414yes—
53C22×C4×D53Q814yes—
54#13133175—232no—
55C2×C4⋊Dic53—22no—
56C2×C4⋊Dic53—22no—
57C2×C4⋊Dic53—22no—
58C2×C4⋊Dic53—24no—
59C2×C4⋊Dic53C2×C414yes—
60C2×#11719919—24no—
61C2×#11719919—24no—
62C2×#11719919—24no—
63C2×#11719921—24no—
64C2×#11719921—24no—
65C2×#11719921—22no—
66C2×#11719921—22no—
67C2×#11719921—24no—
68C2×#11719921—24no—
69C2×#11719921—22no—
70C2×#11719921—22no—
71C2×#11719921—24no—
72C2×#11719921—24no—
73C2×#11719921C2×C414yes—
74C2×#11719921C2×C414yes—
75C2×C4×Dic53—22no—
76C2×C4×Dic53—22no—
77C2×C4×Dic53—24no—
78C2×C4×Dic53—24no—
79C2×C4×Dic53—24no—
80C2×C4×Dic53—24no—
81C2×C4×Dic53—24no—
82C2×C4×Dic53—24no—
83C2×C4×Dic53C2×C414yes—
84C2×C4×Dic53C2×C414yes—
85C2×C4×Dic53D414yes—
86C2×C4×Dic53D414yes—
87#13133124—24no—
88#13133124—22no—
89#13133124—24no—
90#13133124—24no—
91#13133124—24no—
92#13133124—24no—
93C23×C4×C53C2311yescharacteristic
94C23×C4×C53C2312yes—
95C23×C4×C53C2312yes—
96C23×C4×C53C2311yescharacteristic
97C23×C4×C53C2311yescharacteristic
98C2×C4⋊C4×C53—22no—
99C2×C4⋊C4×C53—22no—
100C2×C4⋊C4×C53—22no—
101C2×C4⋊C4×C53—24no—
102C2×C4⋊C4×C53C2×C414yes—
103#95×C53—24no—
104#95×C53—22no—
105#95×C53—24no—
106C24×C53C2411yescharacteristic
107C23×D53—21no—
108C23×D53—21no—
109C23×D53—22no—
110C23×D53—22no—
111C23×D53—22no—
112C23×D53—22no—
113C23×D53—21no—
114C23×D53—21no—
115C23×D53C22×C412yes—
116C23×D53C2×D412yes—
117C23×D53C2×Q812yes—
118C22×C4×C53—21no—
119C22×C4×C53—21no—
120C22×C4×C53—22no—
121C22×C4×C53—22no—
122C22×C4×C53—21no—
123C22×C4×C53—21no—
124C22×C4×C53—22no—
125C22×C4×C53—22no—
126C22×C4×C53—22no—
127C22×C4×C53—22no—
128C22×C4×C53—21no—
129C22×C4×C53—21no—
130C22×C4×C53—22no—
131C22×C4×C53—22no—
132C22×C4×C53—22no—
133C22×C4×C53—22no—
134C22×C4×C53—22no—
135C22×C4×C53—22no—
136C22×C4×C53—22no—
137C22×C4×C53—22no—
138C22×C4×C53—22no—
139C22×C4×C53—22no—
140C22×C4×C53C22×C412yes—
141C22×C4×C53C22×C412yes—
142C22×C4×C53C22×C412yes—
143C22×C4×C53C2×D412yes—
144C22×C4×C53C2×D412yes—
145C22×C4×C53C2×D412yes—
146C22×C4×C53C2×Q812yes—
147C22×C4×C53#4114yes—
148C22×C4×C53#4114yes—
149C22×Dic53—22no—
150C22×Dic53—22no—
151C22×Dic53—22no—
152C22×Dic53—22no—
153C22×Dic53—22no—
154C22×Dic53—22no—
155C22×Dic53—21no—
156C22×Dic53—21no—
157C22×Dic53—22no—
158C22×Dic53—22no—
159C22×Dic53—22no—
160C22×Dic53—22no—
161C22×Dic53—22no—
162C22×Dic53—22no—
163C22×Dic53—22no—
164C22×Dic53—22no—
165C22×Dic53—22no—
166C22×Dic53—22no—
167C22×Dic53C22×C412yes—
168C22×Dic53C22×C412yes—
169C22×Dic53C22×C412yes—
170C22×Dic53C2×D412yes—
171C22×Dic53C2×D412yes—
172C22×Dic53C2×D412yes—
173C22×Dic53C2×D412yes—
174C22×Dic53C2×D412yes—
175C22×Dic53C2×Q812yes—
176C22×Dic53#4114yes—
177C22×Dic53#4114yes—
178C22×Dic53#4112yes—
179C22×Dic53#4112yes—
180C2×C4×D53—28no—
181C2×C4×D53—28no—
182C2×C4×D53—28no—
183C2×C4×D53—28no—
184C2×C4×D53—28no—
185C2×C4×D53—28no—
186C2×C4×D53C4⋊C4116yescomplemented
187C4⋊C4×C53—28no—
188C4⋊C4×C53—28no—
189#11719921—216no—
190#11719921—216no—
191#11719921—28no—
192#11719921—28no—
193C4⋊Dic53—28no—
194C4⋊Dic53—28no—
195#11719919—216no—
196C4×Dic53—28no—
197C4×Dic53—48no—
198C4×Dic53—48no—
199C4×Dic53C22⋊C4116yescomplemented
200C23×C53C23×C411yescharacteristic
201C23×C53C22×D411yescharacteristic
202C23×C53C22×D411yescharacteristic
203C23×C53C22×D411yescharacteristic
204C23×C53C22×Q811yescharacteristic
205C23×C53C2×#4111yescharacteristic
206C23×C53C2×#4111yescharacteristic
207C23×C53C2×#4112yes—
208C23×C53C2×#4112yes—
209C23×C53C2×#4112yes—
210C23×C53C2×#4112yes—
211C22×D53—22no—
212C22×D53—22no—
213C22×D53—24no—
214C22×D53—24no—
215C22×D53—22no—
216C22×D53—22no—
217C22×D53—22no—
218C22×D53—22no—
219C22×D53—24no—
220C22×D53—24no—
221C22×D53—24no—
222C22×D53—24no—
223C22×D53—41no—
224C22×D53—41no—
225C22×D53—42no—
226C22×D53—42no—
227C22×D53—42no—
228C22×D53—42no—
229C22×D53—42no—
230C22×D53—42no—
231C22×D53—41no—
232C22×D53—41no—
233C22×D53C2×C4⋊C414yes—
234C2×C4×C53—22no—
235C2×C4×C53—22no—
236C2×C4×C53—24no—
237C2×C4×C53—22no—
238C2×C4×C53—22no—
239C2×C4×C53—22no—
240C2×C4×C53—22no—
241C2×C4×C53—22no—
242C2×C4×C53—22no—
243C2×C4×C53—24no—
244C2×C4×C53—22no—
245C2×C4×C53—24no—
246C2×C4×C53—24no—
247C2×C4×C53—24no—
248C2×C4×C53—24no—
249C2×C4×C53—24no—
250C2×C4×C53—24no—
251C2×C4×C53—24no—
252C2×C4×C53—42no—
253C2×C4×C53—42no—
254C2×C4×C53—41no—
255C2×C4×C53—41no—
256C2×C4×C53—42no—
257C2×C4×C53—42no—
258C2×C4×C53—42no—
259C2×C4×C53—42no—
260C2×C4×C53—42no—
261C2×C4×C53—42no—
262C2×C4×C53—42no—
263C2×C4×C53C2×C22⋊C414yes—
264C2×C4×C53C2×C4⋊C414yes—
265C2×Dic53—24no—
266C2×Dic53—24no—
267C2×Dic53—22no—
268C2×Dic53—22no—
269C2×Dic53—22no—
270C2×Dic53—24no—
271C2×Dic53—24no—
272C2×Dic53—24no—
273C2×Dic53—24no—
274C2×Dic53—24no—
275C2×Dic53—24no—
276C2×Dic53—24no—
277C2×Dic53—42no—
278C2×Dic53—42no—
279C2×Dic53—42no—
280C2×Dic53—42no—
281C2×Dic53—42no—
282C2×Dic53—42no—
283C2×Dic53—42no—
284C2×Dic53—42no—
285C2×Dic53—41no—
286C2×Dic53—42no—
287C2×Dic53—41no—
288C2×Dic53C2×C22⋊C414yes—
289C2×Dic53C2×C22⋊C414yes—
290C2×Dic53C2×C4⋊C414yes—
291C2×Dic53#11714yes—
292C2×Dic53#12114yes—
293C2×Dic53#12114yes—
294C2×Dic53C22⋊Q814yes—
295C2×Dic53C22⋊Q814yes—
296C4×D53—232no—
297#13852—531nomaximal, Sylow
298C22×C53C22×C22⋊C411yescharacteristic
299C22×C53C22×C4⋊C411yescharacteristic
300C22×C53C2×#11711yescharacteristic
301C22×C53C4×#4112yes—
302C22×C53C4×#4112yes—
303C22×C53C2×#12111yescharacteristic
304C22×C53C2×#12111yescharacteristic
305C22×C53C2×C22⋊Q811yescharacteristic
306C22×C53C2×C22⋊Q811yescharacteristic
307C22×C53#52511yescharacteristic
308C22×C53#52511yescharacteristic
309C22×C53#52512yes—
310C22×C53#52512yes—
311C22×C53#52512yes—
312C22×C53#52912yes—
313C22×C53#52912yes—
314C22×C53#52912yes—
315C22×C53#52912yes—
316C22×C53#53212yes—
317C22×C53#53211yescharacteristic
318C22×C53#53211yescharacteristic
319C22×C53#53312yes—
320C22×C53#53312yes—
321C2×D53—24no—
322C2×D53—28no—
323C2×D53—42no—
324C2×D53—42no—
325C2×D53—44no—
326C2×D53—42no—
327C2×D53—42no—
328C2×D53—44no—
329C2×D53—42no—
330C2×D53—42no—
331C2×D53—44no—
332C4×C53—24no—
333C4×C53—24no—
334C4×C53—44no—
335C4×C53—44no—
336C4×C53—42no—
337Dic53—24no—
338Dic53—44no—
339Dic53—44no—
340Dic53—42no—
341Dic53#38018yes—
342C22×#117—531no—
343C2×C4×C4⋊C4—531no—
344C2×C4×C4⋊C4—531no—
345C2×C4×C22⋊C4—532no—
346#1441—532no—
347#1441—531no—
348#1441D5311yescharacteristic, complemented
349#1439—532no—
350#1439—531no—
351#1439—531no—
352C4×#95—532no—
353C2×C53C2×#38011yescharacteristic
354C2×C53#229612yes—
355C2×C53#229711yescharacteristic
356C2×C53#229711yescharacteristic
357C2×C53#229812yes—
358C2×C53#239211yescharacteristic
359C2×C53#239211yescharacteristic
360C2×C53#239212yes—
361C2×C53#239611yescharacteristic
362C2×C53#239611yescharacteristic
363C2×C53#239612yes—
364D53—44no—
365C24×C4—531no—
366C2×#117—538no—
367C2×#117—1064no—
368C2×#117—1064no—
369C22×C4⋊C4—531no—
370C22×C4⋊C4—532no—
371C22×C4⋊C4—531no—
372C22×C4⋊C4C2×D5311yescharacteristic
373C22×C4⋊C4C2×D5311yescharacteristic
374C22×C22⋊C4—531no—
375C22×C22⋊C4—531no—
376C22×C22⋊C4—532no—
377C22×C22⋊C4—532no—
378C22×C42—531no—
379C22×C42—531no—
380C22×C42—532no—
381C22×C42—532no—
382C4×C4⋊C4—1064no—
383C4×C4⋊C4—1064no—
384C4×C22⋊C4—1068no—
385C2×#95—532no—
386C2×#95—532no—
387C2×#95—532no—
388C2×#95—532no—
389C2×#95—531no—
390C2×#95—532no—
391C2×#95C2×D5312yes—
392C2×#95C2×D5311yescharacteristic
393C2×#95C2×D5312yes—
394C53#1385211yescharacteristic, complemented, Sylow
395C25—531no—
396C23×C4—531no—
397C23×C4—531no—
398C23×C4—534no—
399C23×C4—534no—
400C23×C4—534no—
401C23×C4—531no—
402C23×C4—532no—
403C23×C4—532no—
404C23×C4—1062no—
405C23×C4—1062no—
406C23×C4—1062no—
407C23×C4—1062no—
408C23×C4C22×D5311yescharacteristic
409C23×C4C22×D5312yes—
410C23×C4C22×D5312yes—
411C23×C4C22×D5311yescharacteristic
412C23×C4C22×D5311yescharacteristic
413#117—10632no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—534no—
419C2×C4⋊C4—1062no—
420C2×C4⋊C4—1062no—
421C2×C4⋊C4—1064no—
422C2×C4⋊C4—1064no—
423C2×C4⋊C4—1064no—
424C2×C4⋊C4—1062no—
425C2×C4⋊C4—1064no—
426C2×C4⋊C4C4×D5314yes—
427C2×C22⋊C4—534no—
428C2×C22⋊C4—534no—
429C2×C22⋊C4—1062no—
430C2×C22⋊C4—1062no—
431C2×C22⋊C4—1064no—
432C2×C22⋊C4—1064no—
433C2×C22⋊C4—1064no—
434C2×C22⋊C4—1064no—
435C2×C22⋊C4—1062no—
436C2×C22⋊C4—1062no—
437C2×C22⋊C4—1064no—
438C2×C22⋊C4—1064no—
439C2×C42—534no—
440C2×C42—534no—
441C2×C42—534no—
442C2×C42—534no—
443C2×C42—1062no—
444C2×C42—1062no—
445C2×C42—1064no—
446C2×C42—1064no—
447C2×C42—1064no—
448C2×C42—1064no—
449C2×C42—1064no—
450C2×C42—1064no—
451#95—24no—
452#95—22no—
453#95—24no—
454#95—1064no—
455#95—1064no—
456#95—1064no—
457#95—1064no—
458#95—1062no—
459#95—1064no—
460C24—532no—
461C24—532no—
462C24—532no—
463C24—1061no—
464C24—1061no—
465C24—1062no—
466C24—1062no—
467C24—1061no—
468C24—1061no—
469C24—1062no—
470C24—1062no—
471C24C23×D5311yescharacteristic
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—532no—
495C22×C4—532no—
496C22×C4—532no—
497C22×C4—532no—
498C22×C4—532no—
499C22×C4—532no—
500C22×C4—532no—
501C22×C4—532no—
502C22×C4—532no—
503C22×C4—532no—
504C22×C4—5316no—
505C22×C4—532no—
506C22×C4—534no—
507C22×C4—534no—
508C22×C4—1068no—
509C22×C4—1068no—
510C22×C4—1068no—
511C22×C4—1068no—
512C22×C4—1068no—
513C22×C4—1068no—
514C22×C4—1062no—
515C22×C4—1062no—
516C22×C4—1062no—
517C22×C4—1062no—
518C22×C4—1062no—
519C22×C4—1062no—
520C22×C4—1061no—
521C22×C4—1061no—
522C22×C4—1062no—
523C22×C4—1062no—
524C22×C4—1062no—
525C22×C4—1062no—
526C22×C4—1062no—
527C22×C4—1062no—
528C22×C4—1062no—
529C22×C4—1062no—
530C22×C4—1062no—
531C22×C4—1062no—
532C22×C4C2×C4×D5312yes—
533C22×C4C2×C4×D5312yes—
534C22×C4C2×C4×D5312yes—
535C22×C4D4×D5312yes—
536C22×C4D4×D5312yes—
537C22×C4D4×D5312yes—
538C22×C4#1171994714yes—
539C22×C4Q8×D5312yes—
540C22×C4#1171994914yes—
541C4⋊C4—28no—
542C4⋊C4—28no—
543C4⋊C4—1068no—
544C4⋊C4—10616no—
545C4⋊C4—1068no—
546C22⋊C4—1068no—
547C22⋊C4—10616no—
548C22⋊C4—10616no—
549C22⋊C4—1068no—
550C42—5316no—
551C42—1068no—
552C42—2128no—
553C42—2128no—
554C23—534no—
555C23—1062no—
556C23—1062no—
557C23—1064no—
558C23—1064no—
559C23—1062no—
560C23—1062no—
561C23—1062no—
562C23—1062no—
563C23—1064no—
564C23—1064no—
565C23—1064no—
566C23—1064no—
567C23—2121no—
568C23—2121no—
569C23—2122no—
570C23—2122no—
571C23—2122no—
572C23—2122no—
573C23—2122no—
574C23—2122no—
575C23—2121no—
576C23—2121no—
577C23C22×C4×D5311yescharacteristic
578C23C2×D4×D5311yescharacteristic
579C23C2×D4×D5311yescharacteristic
580C23C2×D4×D5311yescharacteristic
581C23C2×Q8×D5311yescharacteristic
582C23#41×D5311yescharacteristic
583C23#41×D5311yescharacteristic
584C23#41×D5312yes—
585C23#41×D5312yes—
586C23C2×#1171994712yes—
587C23C2×#1171994912yes—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—22no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—534no—
618C2×C4—534no—
619C2×C4—534no—
620C2×C4—534no—
621C2×C4—534no—
622C2×C4—534no—
623C2×C4—534no—
624C2×C4—534no—
625C2×C4—10632no—
626C2×C4—1064no—
627C2×C4—1064no—
628C2×C4—1062no—
629C2×C4—1062no—
630C2×C4—1062no—
631C2×C4—1064no—
632C2×C4—1064no—
633C2×C4—1064no—
634C2×C4—1064no—
635C2×C4—1064no—
636C2×C4—1064no—
637C2×C4—1064no—
638C2×C4—2122no—
639C2×C4—2122no—
640C2×C4—2122no—
641C2×C4—2122no—
642C2×C4—2122no—
643C2×C4—2122no—
644C2×C4—2122no—
645C2×C4—2122no—
646C2×C4—2121no—
647C2×C4—2122no—
648C2×C4—2121no—
649C2×C4C22⋊C4×D5314yes—
650C2×C4C4⋊C4×D5314yes—
651C22—1064no—
652C22—1068no—
653C22—2122no—
654C22—2122no—
655C22—2124no—
656C22—2122no—
657C22—2122no—
658C22—2124no—
659C22—2122no—
660C22—2122no—
661C22—2124no—
662C22C2×C22⋊C4×D5311yescharacteristic
663C22C2×C4⋊C4×D5311yescharacteristic
664C22#117×D5311yescharacteristic
665C22C4×#1171994712yes—
666C22C4×#1171994912yes—
667C22#121×D5311yescharacteristic
668C22#121×D5311yescharacteristic
669C22C22⋊Q8×D5311yescharacteristic
670C22C22⋊Q8×D5311yescharacteristic
671C22#1681112911yescharacteristic
672C22#1681113111yescharacteristic
673C22#1681113312yes—
674C22#1681113612yes—
675C22#1681113612yes—
676C22#1681115012yes—
677C22#1681115612yes—
678C22#1681115812yes—
679C22#1681115912yes—
680C22#1681116812yes—
681C22#1681117211yescharacteristic
682C22#1681117411yescharacteristic
683C22#1681117812yes—
684C22#1681117912yes—
685C4—24no—
686C4—24no—
687C4—44no—
688C4—44no—
689C4—42no—
690C4—538no—
691C4—1064no—
692C4—2124no—
693C4—2124no—
694C4—2122no—
695C2—2124no—
696C2#380×D5311yescharacteristic
697C2#2027719612yes—
698C2#2027720011yescharacteristic
699C2#2027720411yescharacteristic
700C2#2027720712yes—
701C2#2027795411yescharacteristic
702C2#2027795611yescharacteristic
703C2#2027796012yes—
704C2#2027798611yescharacteristic
705C2#2027798811yescharacteristic
706C2#2027799212yes—
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×#1441C2
socle, cosocleC24×C53C24
prime radicalC24×D53C23
hypercenter#1441D53
hypocenterC53#13852
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1441

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic53C2semidirect
3. C2×#16810474C2semidirect
5. #20272968C2semidirect
6. #20272967C2semidirect
10. #95×Dic53C2semidirect
11. C53×#1441C2semidirect
15. C2×#13133175C4semidirect
186. C2×C4×D53C4⋊C4semidirect
199. C4×Dic53C22⋊C4semidirect
348. #1441D53semidirect
394. C53#13852semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#131331752
C2×C4⋊C4×Dic532
C2×#168104742
C2×#168104702
#202729682
#202729672
#202729612
#202729592
#202729572
#95×Dic532
C53×#14412
#1385253